Theorems · Definition · category theory
CategoryTheory.Limits.limit.lift
{J : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} J] →
{C : Type u} →
[inst_1 : CategoryTheory.Category.{v, u} C] →
(F : CategoryTheory.Functor J C) →
[inst_2 : CategoryTheory.Limits.HasLimit F] →
(c : CategoryTheory.Limits.Cone F) → c.pt ⟶ CategoryTheory.Limits.limit FThe morphism from the cone point of any other cone to the limit object.
- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
- CategoryTheory.Limits.Conestatement and proof · cited by 710
- CategoryTheory.Limits.limitstatement · cited by 346
- CategoryTheory.Limits.HasLimitstatement and proof · cited by 226
- CategoryTheory.Limits.IsLimit.liftproof · cited by 167
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
Cited by74
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.limit.lift_πstatement · cited by 266
- CategoryTheory.Limits.prod.liftproof · cited by 123
- CategoryTheory.Limits.pullback.liftproof · cited by 114
- CategoryTheory.Limits.limit.lift_π_assocstatement and proof · cited by 95
- CategoryTheory.Limits.terminal.fromproof · cited by 77
- CategoryTheory.Limits.Pi.liftproof · cited by 53
- CategoryTheory.Limits.equalizer.liftproof · cited by 19
- CategoryTheory.Limits.Multiequalizer.liftproof · cited by 18
- CategoryTheory.Functor.pointwiseRightKanExtensionproof · cited by 13
- CategoryTheory.Limits.WidePullback.liftproof · cited by 12
- CategoryTheory.Limits.limit.preproof · cited by 11
- CategoryTheory.Limits.limit.postproof · cited by 9